Summary of Guarantees For Nonlinear Representation Learning: Non-identical Covariates, Dependent Data, Fewer Samples, by Thomas T. Zhang et al.
Guarantees for Nonlinear Representation Learning: Non-identical Covariates, Dependent Data, Fewer Samples
by Thomas T. Zhang, Bruce D. Lee, Ingvar Ziemann, George J. Pappas, Nikolai Matni
First submitted to arxiv on: 15 Oct 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Systems and Control (eess.SY)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper addresses a key challenge in machine learning: how to extract meaningful features from multiple data sources with different input distributions and possibly dependent data. The authors establish statistical guarantees for learning general nonlinear representations from these sources, which admit different input distributions and are statistically dependent within their source. Specifically, they study the sample-complexity of learning T+1 functions ft(t) ∘ g∗ from a function class F × G, where ft(t) are task-specific linear functions and g∗ is a shared nonlinear representation. The authors show that when N ≧ Cdep(dim(F) + CG/T), the excess risk of ˆf(0) ∘ ˆg on the target task decays as νdiv((dim(F))/N’ + (CG)/NT), where Cdep denotes the effect of data dependency, νdiv denotes a measure of task-diversity between the source and target tasks, and CG denotes the complexity of the representation class G. In particular, their analysis reveals that as the number of tasks T increases, both the sample requirement and risk bound converge to that of r-dimensional regression as if g∗ had been given. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary In this paper, researchers are trying to solve a big problem in machine learning: how to take information from many different places and use it to make good predictions. They’re looking at situations where the data is not all the same, which makes things harder. The authors show that by using certain kinds of models and special techniques, they can learn important features from this kind of data. This could be useful for lots of applications, like recognizing objects in images or understanding language. |
Keywords
» Artificial intelligence » Machine learning » Regression
